Catalytic Effects of Active Site Conformational Change in the Allosteric Activation of Imidazole Glycerol Phosphate Synthase

Imidazole glycerol phosphate synthase (IGPS) is a class-I glutamine amidotransferase (GAT) that hydrolyzes glutamine. Ammonia is produced and transferred to a second active site, where it reacts with N1-(5′-phosphoribosyl)-formimino-5-aminoimidazole-4-carboxamide ribonucleotide (PrFAR) to form precursors to purine and histidine biosynthesis. Binding of PrFAR over 25 Å away from the active site increases glutaminase efficiency by ∼4500-fold, primarily altering the glutamine turnover number. IGPS has been the focus of many studies on allosteric communication; however, atomic details for how the glutamine hydrolysis rate increases in the presence of PrFAR are lacking. We present a density functional theory study on 237-atom active site cluster models of IGPS based on crystallized structures representing the inactive and allosterically active conformations and investigate the multistep reaction leading to thioester formation and ammonia production. The proposed mechanism is supported by similar, well-studied enzyme mechanisms, and the corresponding energy profile is consistent with steady-state kinetic studies of PrFAR + IGPS. Additional active site models are constructed to examine the relationship between active site structural change and transition-state stabilization via energy decomposition schemes. The results reveal that the inactive IGPS conformation does not provide an adequately formed oxyanion hole structure and that repositioning of the oxyanion strand relative to the substrate is vital for a catalysis-competent oxyanion hole, with or without the hVal51 dihedral flip. These findings are valuable for future endeavors in modeling the IGPS allosteric mechanism by providing insight into the atomistic changes required for rate enhancement that can inform suitable reaction coordinates for subsequent investigations.


IGPS active site model components and protonation states
Components of HisF residues 121, 122 and 124 were included to expand the main chain around fGln123 and allow the terminal Cα atoms of this molecular fragment to be frozen.This is done to give the fGln123 residue slight flexibility in geometry optimizations.We included the backbone atoms of His141 since Val140 and Thr142 were also included in the model, therefore we felt truncating at each of those Cα would be more artificial than keeping the His141 backbone and removing the sidechain.Likewise, the portion of the His53 backbone adjacent to Gly52 was kept.This was also decided since we wanted to allow for some flexibility in the oxyanion strand, so we froze the His53 Cα, and left the Gly52 Cα unrestrained.Atoms were constrained using the "-1" optimization flag syntax in Gaussian.This enforces the gradient of these atoms to be 0 during the optimization updates.
The initial protonation states are assumed since hydrogen atoms are not resolved in the X-ray crystal structure.The His178 Nδ protonation state is supported given the position relative to Glu180 in numerous IGPS crystal structures and the expected general acid/base behavior of histidine in enzyme mechanisms involving cysteine catalytic triads. 1 The protonation state of Cys84 is interesting to consider, because it is not necessarily required to reform in the catalytic cycle.Therefore, it is possible Cys84 protonation is obviated during multiple turnover events.A hybrid QM/MM study of a cysteine protease acylation mechanism found the ionic state of the Cys-His dyad (Cys -, HisH + ) to be more stable in the free enzyme, whereas binding of the substrate shifted the equilibrium such that the neutral dyad became more stable. 2u180 hydrogen bonds with His178 in all structures and remains in the carboxylate form for the results discussed here.Int1 geometries with a Glu180 carboxylic acid were evaluated and the difference in protonation was not found to alter any mechanistic conclusions.Furthermore, site-directed mutagenesis experiments support a mechanism where Glu180 serves a structural role to position His178, as opposed to directly effecting catalysis.Legend: SP1: B3LYP-D3BJ/6-311+G(2d,2p), using IEF-PCM with solvent=diethylether SP2: ωB97X-D/6-311+G(2d,2p), using IEF-PCM with solvent=diethylether SP3: ωB97X-D/def2QZVPP, using IEF-PCM with solvent=diethylether The Active-ES, Active-TS3 and Active-TS4 structures were selected to evaluate the functional sensitivity and solvent effects on geometries and energies.The energies reported in the main text are obtained from the GO1//SP1 level.This was chosen since it was the most consistent with the available experimental data.In all variations TS4 is identified as the rate limiting step.The ωB97X-D (GO1) and B3LYP-D3BJ (GO2) geometry optimizations are consistent in both structure (all atom RMSDs < 0.1 Å) and energies (∆∆E < 1 kcal/mol for TS3 and TS4).The difference in barriers from these optimized geometries after single point energy refinement (GO1//SP1 and GO2//SP1) are 1.12 kcal/mol and 0.24 kcal/mol for TS3 and TS4, respectively, and TS4 remains the rate-limiting TS.
The standard, and generally well-accepted, approach in truncated enzyme models is to perform gas phase geometry optimizations. 5evertheless, solvent effects on the geometries may be important to consider especially for charge-separated transition states.Therefore, we reoptimized the ES, TS3 and TS4 of the Active model with implicit solvent.We encountered numerous convergence issues while attempting to optimize with the IEF-PCM method, however we were successful with CPCM (solvent = diethylether).The difference in energy barriers measured from ES when including solvent effects (GO3) is very minimal (∆∆E TS3 = -0.15kcal/mol and ∆∆E TS4 = -0.56kcal/mol), even though there are subtle structural changes, as measured by all-atom RMSDs: ES=0.207,TS3=0.087,TS4=0.107.After single-point energy corrections on the solvent optimized geometries (GO3//SP1) there are minimal energy differences (∆∆E TS3 = 0.70 kcal/mol and ∆∆E TS4 = 0.99 kcal/mol) that do not alter any discussion or conclusions in the main text.

Summary of this work in relation to previous studies
. Energy surface summary of this work in relation to previous studies.
Steered molecular dynamics studies performed by Osuna and coworkers 8 evaluated the free energy barrier of a Val51 dihedral flip in IGPS simulations of varying substrate bound states.They estimated the conformational barrier to be 22 kcal/mol in the -PrFAR/+Gln state (red dashed line), consistent with the basal activity measured from experiments. Teir result in conjunction with the high Inactive barrier calculated here support a basal reaction that is rate limited by conformational change.In the +PrFAR/+Gln state the Val51 dihedral rotation barrier was reduced to 8 kcal/mol (green dashed line), much lower than the experimental Gln hydrolysis rate indicating a chemical transformation is rate limiting in the presence of PrFAR.
c The 15 N kinetic isotope effect (KIE) was measured in carbamoyl phosphate synthetase (CPS), a class-I GAT similar to IGPS, to investigate the rate limiting step of glutamine hydrolysis in the presence and absence of the reaction activators CO3 -and MgATP. 9he glutamine substrate 15 N KIE in the presence of activators was measured to be 1.023, which is close to the KIE of 1.025 observed from organic model reactions in which the C-N bond breaking is known to be rate-determining. 10This translates to TS4 as the rate limiting step in Gln hydrolysis by IGPS in the presence of PrFAR (green box).In the absence of the CPS activators, the 15 N isotope effect is reduced by 1.57%, and the authors predict the rate limiting step to occur prior to ammonia release (red box).

NBO calculation details and data
The ES, TS2, TS3 and TS4 stationary points were optimized in Inactive fGln123 and Inactive Val51.Energy barriers were calculated for each TS relative to the ES structure of the corresponding model.The stabilizing oxyanion hole strength was evaluated in each TS by donor-acceptor interactions of Leu85, Gly52 and Val51 with the Gln Oε lone pair electrons via Natural Bonding Orbital (NBO) second-order perturbation theory analysis version 7.0.5. 11 The stabilization energies of oxyanion hole residues in TS2 (Figure S4) are highly consistent with the results from TS3 shown in the main text, however since only two Gln Oε lone-pair electrons were identified in each TS2 structure the total contributions from each residue are smaller in magnitude compared to the TS3 results with three lone-pairs.
The stabilization energies of oxyanion hole residues in TS4 (Figure S5) reveal that the Val51 N-H in the Active and Inactive fGln123 models no longer interacts with Gln Oε lone-pair electrons.Instead, the N-H shifts to interact with the new lone pair electrons on the His178 Nε.This results in oxyanion hole stabilization energy contributions to be nearly identical in Active-TS4, Inactive fGln123-TS4 and Inactive Val51-TS4.Table S4.Interactions between oxyanion hole components and Gln Oε lone pair electrons.A value of 0 arises if there is either no interaction or the strength of that interaction is below the calculation cutoff (0.05 kcal/mol)."n/a" indicates the corresponding lone pair electrons were either not detected in the structures or were delocalized into antibonding orbitals connected to the Gln substrate.

Decomposition of fGln123 interaction energy
The proximity of fGln123 to the HisH active site is another structural feature influenced by the binding of the allosteric effector, PrFAR.It is expected that fGln123 assists in recruiting and stabilizing the glutamine substrate, but it is unclear to what extent, if any, this proximity influences the chemical coordinate.The Inactive fGln123 oxyanion hole contributions (Figure 5, SI Figures S4-S5) are nearly identical to Active, with an average difference of less than 0.2 kcal/mol per residue in each TS (Table S4).Therefore, the oxyanion hole stabilization is not influenced by the proximity of fGln123.
To better understand how fGln123 influences the pathway energetics, we evaluated the interaction energy between the fGln123 molecular fragment and the rest of the active site residues for the Active, Inactive fGln123, Inactive Val51 and Inactive models.
The different positions of fGln123 are displayed in Figure S8.
The fGln123 interaction energy results are summarized in Figure S7 and reported in Table S5.The total interaction energy (Total INT) in ES is much more favorable when fGln123 is closer to the active site.Active-and Inactive Val51-ES have similar fGln123 interaction energies of -29.

Model construction and structural comparisonsFigure S1 .
Figure S1.Geometric comparisons of the (A) Active and (B) Inactive models.Coordinates from each model are taken from their optimized ES structures.Inactive differs from Active mainly in the proximity of fGln123, positioning of the oxyanion strand, and backbone dihedral of Val51.

Figure S2 .
Figure S2.Geometric comparisons of the (A) Active and (B) Inactive Val51 models.Coordinates from each model are taken from their optimized ES structures.Inactive Val51 differs from Active in the backbone dihedral of Val51.All carbons frozen during optimization are in the same positions between the two models.

Figure S3 .
Figure S3.Geometric comparisons of the (A) Active and (B) Inactive fGln123 models.Coordinates from each model are taken from their optimized ES structures.Inactive fGln123 differs from Active in the proximity of fGln123.

Figure S5 .
Figure S5.Oxyanion stabilizing interaction energies between Gln Oε lone pair electrons and  * orbitals from Val51, Gly52 and Leu85 in TS2 measured by second order perturbations in the NBO basis.Reduced ball and stick representations of the Active, Inactive fGln123, Inactive Val51 and Inactive TS2 structures of relevant model components to aid visualizations.Distances between the Gln Oε and backbone H atoms of Val51, Gly52 and Leu85 are shown in Å. Active and Inactive fGln123 correspond to models with the Val51 N-H pointing into the active site.Inactive Val51 and Inactive correspond to models with the Val51 N-H directed outwards.

Figure S6 .
Figure S6.Oxyanion stabilizing interaction energies between Gln Oε lone pair electrons and  * orbitals from Val51, Gly52 and Leu85 in TS4 measured by second order perturbations in the NBO basis.Reduced ball and stick representations of the Active, Inactive fGln123, Inactive Val51 and Inactive TS4 structures of relevant model components to aid visualizations.Distances between the Gln Oε and backbone H atoms of Val51, Gly52 and Leu85 are shown in Å. Active and Inactive fGln123 correspond to models with the Val51 N-H pointing into the active site.Inactive Val51 and Inactive correspond to models with the Val51 N-H directed outwards.
2 and -30.6 kcal/mol, which are much lower than the Inactive fGln123 and Inactive values (-5.4 and -13.1 kcal/mol, respectively).The difference in fGln123 interaction energy between Inactive fGln123 and Inactive can be reasoned by the presence of a hydrogen bond between the sidechain NH2 group of fGln123 and the backbone carbonyl oxygen of Val140 (FigureS9) that is present in the Inactive model but absent in the Inactive fGln123model.

Figure S7 .
Figure S7.Decomposition of interaction energy calculated with ALMO-EDA between fGln123 and the HisH active site in the optimized ES complex for each QM model.The interaction energy in Inactive Val51 becomes slightly less favorable in TS2, TS3, and TS4 because the Gly52 backbone shifts away from fGln123 to interact more strongly with the Gln Oε.The Inactive model also shows interaction energy changes between ES and TS2, TS3, and TS4, because the Gln substrate moves farther from fGln123 to react with Cys84.The Active and Inactive fGln123 models have minimal structural rearrangements along the reaction coordinate; therefore, the fGln123 interaction energy values are consistent across the evaluated structures.

Figure S8 .
Figure S8.Distances from the frozen Cys84 Cα atom to the frozen fGly121 and fAla124 Cα atoms in A) Active, B) Inactive and C) Inactive fGln123.These distances cannot change during geometry optimizations.

Figure S9 .
Figure S9.Differences of fGln123 interactions in the ES structure of each active site model that effect the fGln123 total interaction energy.Any atom that is not transparent is within 3 Å of an atom in the fGln123 molecular fragment, and it labeled.The hydrogen bond to Val140 is not present in crystal structures (fGln123:N-hVal140:O distance of 5.3 Å in 7ac8 chains C/D) because of a change in the fGln123 rotamer state during geometry optimization.The optimized rotamer state in the Inactive model is structurally feasible due to the open dimer interface in the inactive conformation crystal structure, however it cannot be ruled out that it may be a consequence of the truncated model used here.In the Inactive model, fGln123 forms a single hydrogen bond (1.85 Å) with its NH2 group and the backbone carbonyl oxygen of Val140.In contrast, fGln123 in the Inactive fGln123 model does not form hydrogen bonds with other active site residues in any of the optimized structures.The presence of this hydrogen bond is likely the reason why the fGln123 interaction energy is more favorable in the Inactive model than the Inactive fGln123 construct, as

Figure S10 .
Figure S10.Optimized IGPS geometries of Active-ES (left) and Inactive Val51-ES (right) models aligned to crystallographic models of PLP synthase (PDB: 2NV2, 14 transparent) and CPS (PDB: 1C3O, 15 transparent) via Gln substrate carboxamide atoms.The preformed oxyanion holes from PLP and CPS are more structurally consistent with the IGPS Gly52 than with Val51, especially in the manually constructed Inactive Val51 model.Interestingly, the backbone dihedral of Gly47 in PLP synthase rotates upon dimer complexation and Gln binding, similar to what is proposed for Val51 in IGPS upon PrFAR binding.The H atoms of PLP synthase Gly47 and CPS Gly241 were added with the PyMol add_hydrogen function since they are not resolved in the crystal structures.Hydrogen bond distances are shown in Å and are in parentheses for the non-optimized structures.

Table S1 .
IGPS active site models from PDB 7ac8 chains C/D (Inactive model) and E/F (Active model)

Table S2 .
4eometry optimizations (GO) at different levels of theory.Energies shown in kcal/mol.RMSDs calculated from all atoms using VMD and shown in Å.4

Table S3 .
Single point (SP) corrections at different levels of theory.Energies shown in kcal/mol.

Table S5 .
fGln123 interaction energies for ES structures measured with ALMO-EDA.